Linear Algebra in Physical Science and Engineering: Theory and Applications

[cgw]

I was wondering who takes linear algebra as an undergrad course. I assume math majors but maybe it is not required. I am studying it because I think it will help me understand quantum mechanics better. As soon as I got into it I realized that it is pretty usefull in general (engineering etc). I wish I had taken it in school.

 

[mathwonk]

linear algebra is the most universally useful mathematics subject, in all fields. It is also the easiest, and most computable, which is main reason it is useful. another reason is that almost all problems can be approximated by linear problems, whose solutions then provide approximations to the actual solutions. this is the fundamental idea of differential calculus. for quantum mechanics one needs infinite dimensional linear algebra, so it is crucial to learn the abstract structure of the subject to understand the infinite dimensional generalizations.

 

[CompuChip]

At my university, Linear Algebra is given in the first semester of the first year and required for all Mathematics and Physics students. I cannot imagine there are universities where this is different. I know of many other bachelors (Chemistry, Pharmacy, Computer Science and other exact studies) that have a required "mathematics for <...fill in profession>" course of which linear algebra is also a large part (together with calculus).

 

[mda]

how about all of the above?

 

[haushofer]

At my university it's a first semester course for mathematicians and (applied) physicists :)

 

[mathwonk]

who wears short shorts? duh doot duh doot duh dood dah.

 

[CompuChip]

I do :tongue:
Do you have the tune to that song (duh doot duh ... )?

 

[mathwonk]

that part was just a little saxophone riff, rising for the first 4 notes, then back down.

 

[Pollywoggy]

linear algebra

I am not sure what the poll question is asking. I don't go to school but one of the books I am reading is a book about linear algebra. Many of the quantum mechanics books I have seen use matrix algebra and I remember when I took an electronics course many years ago, I saw matrices for the first time. Linear algebra seems to be important in many fields.

 

[GreenMind]

At my University it seems as though only Math Majors and Engineering Majors take this course. Although not required for Engineering major, most student opt to take this course to receive a MATH minor.

 

[Mystic998]

All of the above. If not in a specific linear algebra/matrix algebra course, then as part of some other course.

 

[RasslinGod]

as a physics major, I am curious, how does linear algebra relate to physics?? I am in my 3rd week of LA this semester, and I am really dying to see how this appleis to physics.

 

[CompuChip]

How doesn't it? All of physics is about relating phenomena in different coordinate systems (e.g. if the laws of classical mechanics would depend on a choice of basis vectors, then you and I would probably choose different ones and observe different things, therefore a physical theory better be insensitive to this), superposition principles (the electric field of two charges is the field of one vector sum field of the other), independence (from independence of certain quantities on one of the coordinates we can for example find constants of motion, such as momentum conservation), and most physical laws are (initially) expressed in inner and outer products (think $\vec F = q (\vec E + \vec v \times \vec B)$ and $W = \vec F \cdot \vec d = F d \cos\theta$).

 

[BryanP]

linear algebra is required in both math majors at UC berkeley

 

[ejungkurth]

Imagine my surprise as I showed up for Linear Algebra courses only to find that I was the only one, including the professor.

As it turns out, linear algebra is incredibly important to computer science, let alone its theoretical aspects in various fields. You will find on inspection that modern microprocessor design yields in many respects to matrix algebra.

Do not underestimate the impact of linear algebra on microprocessor design or you will be inestimably behind the curve.

You have to understand sparse matrixes or you will not be able to understand caching as it has been currently been implemented in modern microprocessors.

 

[jimisrv]

I would assume that all physical science/engineering majors are at least exposed to linear algebra in an applied context (in the sense of solving linear equations, determinants, Eigen value problems, linear vector ODE's etc.). Physics, math, EE, Econ, ME all generally offer more advanced upper division elective courses (usually called "mathematical methods in...") that one takes down the line (after initial math sequences) where the stress is in abstract formulations. In fact, understanding the theory deeply enables one to learn more exotic tools (such as functional analysis for example). A mathematician will probably take an abstract linear algebra course as his/her first demanding proof writing course, which they will absolutely be required to take.

This material is highly useful for both theoretical subjects and applications (arguably more so than calculus). As an example (and my area of study coincidentally), one might be interested in steering an aircraft from one point to another, maybe with an autopilot that you as an engineer design. The physics of motion are going to depend on the state of your aircraft (ie orientation, velocity, throttle, rudder angle etc), something that you as an engineer might have control of. The physics of motion, that you might be familiar in the context of a falling apple (F = ma), are in fact (well a little simplified) encoded in a matrix. This is because there are multiple factors that influence the physics, and multiple factors that describe the physics (motion, ie velocity in x,y,z, angle about x,y,z etc), giving the familiar x=Ay. Thus, solving for the trajectory involves solving linear equations (linear ODE's to be precise).